In this paper we study the spatial behavior of the steady-state solutions for the approach of thin thermoelastic plates developed by Lagnese and Lions [J.E. Lagnese, J.-L. Lions, Modelling, Analysis and Control of Thin Plates, Collection RMA, vol. 6, Masson, Paris, 1988]. The model leads to a coupled complex system of partial differential equations, one of fourth order in terms of the amplitude of the vertical deflection and the other of second-order in terms of the amplitude of temperature field. Coupling in an appropriate way the two equations in an integral identity we are able to identify some cross-sectional line integral measures associated with the amplitudes of the vertical deflection and temperature vibrations, provided that the exciting frequency is less than a certain critical frequency. Furthermore, we are able to establish a second-order differential inequality whose integration furnishes a Saint-Venant type decay estimate for a bounded strip and an alternative of Phragmen-Lindelof type for a semi-infinite strip. The critical frequency is individuated by means of the use of some Wirtinger and Knowles inequalities.

Convexity considerations and spatial behavior for the harmonic vibrations in thermoelastic plates

D'APICE, Ciro
2005-01-01

Abstract

In this paper we study the spatial behavior of the steady-state solutions for the approach of thin thermoelastic plates developed by Lagnese and Lions [J.E. Lagnese, J.-L. Lions, Modelling, Analysis and Control of Thin Plates, Collection RMA, vol. 6, Masson, Paris, 1988]. The model leads to a coupled complex system of partial differential equations, one of fourth order in terms of the amplitude of the vertical deflection and the other of second-order in terms of the amplitude of temperature field. Coupling in an appropriate way the two equations in an integral identity we are able to identify some cross-sectional line integral measures associated with the amplitudes of the vertical deflection and temperature vibrations, provided that the exciting frequency is less than a certain critical frequency. Furthermore, we are able to establish a second-order differential inequality whose integration furnishes a Saint-Venant type decay estimate for a bounded strip and an alternative of Phragmen-Lindelof type for a semi-infinite strip. The critical frequency is individuated by means of the use of some Wirtinger and Knowles inequalities.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1212040
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